Research Article
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Year 2024, , 267 - 276, 23.04.2024
https://doi.org/10.36890/iejg.1454012

Abstract

References

  • [1] Bejancu, A.: CR-submanifolds of a Kähler manifold I. Proc. Amer. Math. Soc. 69, 135-142 (1978).
  • [2] Chen, B.-Y., Deshmukh, S.: Yamabe and quasi-Yamabe solitons on Euclidean submanifolds. Mediterr. J. Math. 15 (194), (2018).
  • [3] Chen, B.-Y., Djoric, M. B., Djoric, M.: Quasi-Yamabe and Yamabe solitons on hypersurfaces of nearly Kähler manifolds. Mediterr. J. Math. 21 (10), (2024).
  • [4] Cho, J. T., Kimura, M.: Ricci solitons and real hypersurfaces in a complex space form. Tohoku Math. J. 61 (2), 205-212 (2009).
  • [5] Cho, J. T., Kimura, M.: Ricci solitons of compact real hypersurfaces in Kähler manifolds. Math. Nachr. 284 (11-12), 1385-1393 (2011).
  • [6] Djoric, M., Okumura, M.: Certain CR submanifolds of maximal CR dimension of complex space forms. Differential Geom. Appl. 26, 208-217 (2008).
  • [7] Djoric, M., Okumura, M.: Scalar curvature of CR submanifolds of maximal CR dimension of complex projective space. Monatsh. Math. 154, 11-17 (2008).
  • [8] Djoric, M., Okumura, M.: CR submanifolds of complex projective space. Developments in Mathematics. 19 Springer, New York (2009).
  • [9] Hamilton, R. S.: The Ricci flow on surfaces. Math. Gen. Relativ. (Santa Cruz, CA, 1986), Contemp. Math. 71 Amer. Math. Soc. 237-262 (1988).
  • [10] Huang, G., Li, H.: On a classification of the quasi Yamabe gradient solitons. Methods Appl. Anal. 21 (3), 379-389 (2014).
  • [11] Kawamoto, S.: Codimension reduction for real submanifolds of complex hyperbolic space. Revista Mathematica de la Universidad Complutense de Madrid 7, 119-128 (1994).
  • [12] Leandro, B., Pina, H.: Generalized quasi Yamabe gradient solitons. J. Diff. Geom. Appl. 49, 167-175 (2016).
  • [13] Lee, J. M., Parker, T. H.: The Yamabe problem, Bull of Amer. Math. Soc. 17 (1), 37-91 (1987).
  • [14] Montiel, S., Romero, A.: On some real hypersurfaces of a complex hyperbolic space. Geom. Dedicata 20, 245-261 (1986).
  • [15] Niebergall, R., Ryan, P. J.: Real hypersurfaces in complex space forms. In: Tight and taut submanifolds. (eds. T. E. Cecil and S.-S. Chern) Math. Sci. Res. Inst. Publ. 32 Cambridge University Press, Cambridge 233-305 (1997).
  • [16] Okumura, M.: On some real hypersurfaces of a complex projective space. Trans. Amer. Math. Soc. 212, 355-364 (1975).
  • [17] Okumura, M.: Codimension reduction problem for real submanifolds of complex projective space. Colloq. Math. Soc. János Bolyai 56, 574-585 (1989).

Quasi Yamabe Solitons on CR Submanifolds of Maximal CR Dimension in Kähler Manifolds

Year 2024, , 267 - 276, 23.04.2024
https://doi.org/10.36890/iejg.1454012

Abstract

In this paper we give necessary and sufficient conditions for a CR submanifold of maximal CR
dimension in arbitrary Kähler manifold to admit (quasi-)Yamabe structure, with naturally chosen
soliton vector field. When the ambient manifold is a non-flat complex space form, we give a
complete classification of such solitons, under certain conditions.

References

  • [1] Bejancu, A.: CR-submanifolds of a Kähler manifold I. Proc. Amer. Math. Soc. 69, 135-142 (1978).
  • [2] Chen, B.-Y., Deshmukh, S.: Yamabe and quasi-Yamabe solitons on Euclidean submanifolds. Mediterr. J. Math. 15 (194), (2018).
  • [3] Chen, B.-Y., Djoric, M. B., Djoric, M.: Quasi-Yamabe and Yamabe solitons on hypersurfaces of nearly Kähler manifolds. Mediterr. J. Math. 21 (10), (2024).
  • [4] Cho, J. T., Kimura, M.: Ricci solitons and real hypersurfaces in a complex space form. Tohoku Math. J. 61 (2), 205-212 (2009).
  • [5] Cho, J. T., Kimura, M.: Ricci solitons of compact real hypersurfaces in Kähler manifolds. Math. Nachr. 284 (11-12), 1385-1393 (2011).
  • [6] Djoric, M., Okumura, M.: Certain CR submanifolds of maximal CR dimension of complex space forms. Differential Geom. Appl. 26, 208-217 (2008).
  • [7] Djoric, M., Okumura, M.: Scalar curvature of CR submanifolds of maximal CR dimension of complex projective space. Monatsh. Math. 154, 11-17 (2008).
  • [8] Djoric, M., Okumura, M.: CR submanifolds of complex projective space. Developments in Mathematics. 19 Springer, New York (2009).
  • [9] Hamilton, R. S.: The Ricci flow on surfaces. Math. Gen. Relativ. (Santa Cruz, CA, 1986), Contemp. Math. 71 Amer. Math. Soc. 237-262 (1988).
  • [10] Huang, G., Li, H.: On a classification of the quasi Yamabe gradient solitons. Methods Appl. Anal. 21 (3), 379-389 (2014).
  • [11] Kawamoto, S.: Codimension reduction for real submanifolds of complex hyperbolic space. Revista Mathematica de la Universidad Complutense de Madrid 7, 119-128 (1994).
  • [12] Leandro, B., Pina, H.: Generalized quasi Yamabe gradient solitons. J. Diff. Geom. Appl. 49, 167-175 (2016).
  • [13] Lee, J. M., Parker, T. H.: The Yamabe problem, Bull of Amer. Math. Soc. 17 (1), 37-91 (1987).
  • [14] Montiel, S., Romero, A.: On some real hypersurfaces of a complex hyperbolic space. Geom. Dedicata 20, 245-261 (1986).
  • [15] Niebergall, R., Ryan, P. J.: Real hypersurfaces in complex space forms. In: Tight and taut submanifolds. (eds. T. E. Cecil and S.-S. Chern) Math. Sci. Res. Inst. Publ. 32 Cambridge University Press, Cambridge 233-305 (1997).
  • [16] Okumura, M.: On some real hypersurfaces of a complex projective space. Trans. Amer. Math. Soc. 212, 355-364 (1975).
  • [17] Okumura, M.: Codimension reduction problem for real submanifolds of complex projective space. Colloq. Math. Soc. János Bolyai 56, 574-585 (1989).
There are 17 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Article
Authors

Milos B Djoric 0000-0001-5462-5522

Mirjana Djoric 0000-0003-3915-2928

Early Pub Date April 15, 2024
Publication Date April 23, 2024
Submission Date March 17, 2024
Acceptance Date April 7, 2024
Published in Issue Year 2024

Cite

APA Djoric, M. B., & Djoric, M. (2024). Quasi Yamabe Solitons on CR Submanifolds of Maximal CR Dimension in Kähler Manifolds. International Electronic Journal of Geometry, 17(1), 267-276. https://doi.org/10.36890/iejg.1454012
AMA Djoric MB, Djoric M. Quasi Yamabe Solitons on CR Submanifolds of Maximal CR Dimension in Kähler Manifolds. Int. Electron. J. Geom. April 2024;17(1):267-276. doi:10.36890/iejg.1454012
Chicago Djoric, Milos B, and Mirjana Djoric. “Quasi Yamabe Solitons on CR Submanifolds of Maximal CR Dimension in Kähler Manifolds”. International Electronic Journal of Geometry 17, no. 1 (April 2024): 267-76. https://doi.org/10.36890/iejg.1454012.
EndNote Djoric MB, Djoric M (April 1, 2024) Quasi Yamabe Solitons on CR Submanifolds of Maximal CR Dimension in Kähler Manifolds. International Electronic Journal of Geometry 17 1 267–276.
IEEE M. B. Djoric and M. Djoric, “Quasi Yamabe Solitons on CR Submanifolds of Maximal CR Dimension in Kähler Manifolds”, Int. Electron. J. Geom., vol. 17, no. 1, pp. 267–276, 2024, doi: 10.36890/iejg.1454012.
ISNAD Djoric, Milos B - Djoric, Mirjana. “Quasi Yamabe Solitons on CR Submanifolds of Maximal CR Dimension in Kähler Manifolds”. International Electronic Journal of Geometry 17/1 (April 2024), 267-276. https://doi.org/10.36890/iejg.1454012.
JAMA Djoric MB, Djoric M. Quasi Yamabe Solitons on CR Submanifolds of Maximal CR Dimension in Kähler Manifolds. Int. Electron. J. Geom. 2024;17:267–276.
MLA Djoric, Milos B and Mirjana Djoric. “Quasi Yamabe Solitons on CR Submanifolds of Maximal CR Dimension in Kähler Manifolds”. International Electronic Journal of Geometry, vol. 17, no. 1, 2024, pp. 267-76, doi:10.36890/iejg.1454012.
Vancouver Djoric MB, Djoric M. Quasi Yamabe Solitons on CR Submanifolds of Maximal CR Dimension in Kähler Manifolds. Int. Electron. J. Geom. 2024;17(1):267-76.